Consider a balloon. I don’t imagine in visuals but if you do, either a solid color or a patterned balloon works. Let’s say it’s a cow print design.

Deflate it, then stretch the balloon over a vacuum cleaner tube and put on a rubber band to keep it in place.

If you pour sand on it, you can only get a small bump of sand and then it’ll run off the sides. Reasonable, logical, normal behavior. Clearly it’s a surface — it’s holding sand, it’s pouring sand in different directions over the edge, the sand is not all compacted into a single grain.

Turn on the vacuum cleaner. Assume a balloon stretchier than the strongest vacuum cleaner in the universe. What happens? Several things, each of which are perfectly reasonable:

1) The end of the tube is still a circle, and the balloon is still attached and covering the tube, so it’s still a two-dimensional circle.

2) A single grain of sand can’t block the vacuum tube, so it clearly hasn’t collapsed to a point.

3) The covered end of the vacuum cleaner tube is still the same circle, with the same diameter, as it was before you turned on the vacuum.

4) You can pour buckets more of sand onto that stretched circle of balloon than the handful you could before.

5) If you pour enough sand onto the circle, it’ll behave just like it did before: the sand will form a small mound and then newly-poured sand will run off whichever side the sand was poured on.

6) The rubber band is going to catch some of the overflowing grains of sand and hold onto them (‘accretion’), near but just outside the circle.

Next: Consider a more powerful vacuum cleaner. How much more? Lots. The most. An atomic Dyson powered by nuclear fusion. (This is a bit unrealistic, but that’s astrophysics for you.)

How much sand can you pour onto that two-dimensional, circular, balloon surface?

Lots. The most. Some of it will spill around the edges and get caught in the accretion band, but somehow that circle, that’s still the same size and clearly still blocking the vacuum tube, can hold an entire universe of sand.

That’s how black holes work :)

ps. For those who dislike the crudity of my teaching analogy and want to pop the spherical cow balloon: Topologically, the surface covering the vacuum tube is always a circle, even if you have an infinitely-powerful vacuum cleaner. At no point — pun intended — can a vacuum cleaner apply a transformation applied that reduces the dimensionality of the surface, thus it must remain, topologically, a circle.

pps. So clearly I must choose the circle in front of me! Hahaha! Aaaahahahah!

ppps. dies